Question

Hey, need help with a parabola equation. I'm given 4x^2-8x-y^2-6y=9. I need to find the foci. Can anyone help? I'm horrible at math :/

Answer 1

I know I need to factor and get it into the form of (y+-b)^2=k(x+-a)... but how? and then how do I get the foci from that?

Answer 2

idk if this is wat u want :
4x²-8x=y²-6y+9
factorise:
4x(x-2)=(y-3)²

Answer 3

thank you for the reply :). only thing is, how do I find the foci now? I had a bad teacher and he never explained this...

Answer 4

\[4x^2-8x-y^2-6y=9\]\[4x^2-8x+4-y^2-6y-9=4\]\[4(x-1)^2-(y+3)^2=4\]\[(x-1)^2-\frac{(y+3)^2}{2^2}=1\quad\mbox{-hyperbola}\]\[\mbox{center: }(1,-3)\quad,\quad a=1\quad,\quad b=2\]\[F_{1,2}=(1\pm\sqrt{a^2+b^2},-3)=(1\pm\sqrt{5},-3)\] http://www.wolframalpha.com/input/?i=4x%5E2-8x-y%5E2-6y%3D9

Answer 5

can i ask where u find the value of a and b?

Answer 6

\[\frac{(x-p)^2}{a^2}-\frac{(y-q)^2}{b^2}=1\]

Answer 7

Ah, nice, thanks ^^